Problem: If four times the reciprocal of the circumference of a circle equals the diameter of the circle, then the area of the circle is
Answer Choices:
A. 1π2\dfrac{1}{\pi^{2}}π21​
B. 1π\dfrac{1}{\pi}π1​
C. 111
D. π\piπ
E. π2\pi^{2}π2 Solution:
If rrr and AAA are the radius and area of the circle, respectively, then
42πr=2r4=4πr21=πr2=A.\begin{aligned} \dfrac{4}{2 \pi r} & =2 r \\ 4 & =4 \pi r^{2} \\ 1 & =\pi r^{2}=A . \end{aligned} 2πr4​41​=2r=4πr2=πr2=A.​